A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00 p.m. on Wednesday, what is the correct time ?
- (a) 5:36 p.m. ✓ UPSC's answer
- (b) 5:30 p.m.
- (c) 5:24 p.m.
- (d) 5:18 p.m.
Why the answer is (a)
• The clock is set correctly at 8:00 a.m. on Monday and shows 6:00 p.m. on Wednesday, which is a duration of 56 hours according to the fast clock.
• In 24 hours of real time, the fast clock gains 10 minutes, meaning it covers 24 hours and 10 minutes (1450 minutes) of its own time.
• Therefore, the ratio of fast clock time to real time is 1450 minutes (fast) to 1440 minutes (real), or 29:28.
• Let the real time elapsed be $x$ minutes. The relationship is $\frac{1450}{1440} = \frac{56 \times 60}{x}$.
• Solving for $x$: $x = \frac{1440 \times 3360}{1450} = \frac{144 \times 3360}{145} = \frac{483840}{145} \approx 3336.82$ minutes.
• 3336.82 minutes is approximately 55 hours and 36.82 minutes. Adding this to the start time of 8:00 a.m. Monday gives a correct time of approximately 5:36 p.m. on Wednesday.
Why the other options are wrong
- (b) 5:30 p.m.
- This option incorrectly assumes a linear gain of 10 minutes per 24 hours without accounting for the fact that the clock's speed is constant relative to real time, leading to a miscalculation of the proportion.
- (c) 5:24 p.m.
- This option likely results from using an incorrect ratio or rounding error in the calculation of the real time elapsed.
- (d) 5:18 p.m.
- This option is derived from an incorrect assumption about the rate of gain or a calculation error in converting the total minutes back to hours and minutes.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.